Films transport through

This leads to rate equations with constant mass transfer coefficients, whereas the effect of net transport through the film is reflected separately in thej/gj and Y factors. For unidirectional mass transfer through a stagnant gas the rate equation becomes... 

Although microporous membranes are a topic of research interest, all current commercial gas separations are based on the fourth type of mechanism shown in Figure 36, namely diffusion through dense polymer films. Gas transport through dense polymer membranes is governed by equation 8 where is the flux of component /,andare the partial pressure of the component i on either side of the membrane, /is the membrane thickness, and is a constant called the membrane permeability, which is a measure of the membrane s ability to permeate gas. The ability of a membrane to separate two gases, i and is the ratio of their permeabilities,a, called the membrane selectivity (eq. 9). 

All reactions in which charge is transported through a film of reaction product on the metal surface —the film may or may not be rate determining (e.g. parabolic, logarithmic, asymptotic, etc. or linear growth laws, respectively). 

An important feature of such films is their low ionic conductivity that restricts cation transport through the film substance. Electronic semiconduction, however, permits other electrode processes (oxidation of H2O to O2) to take place at the surface without further significant film growth. At elevated anodic potentials adsorption and entry of anions, particularly chloride ions, may lead to instability and breakdown of these protective films (Sections 1.5 and 1.6). 

Regarding the question of the rate of electron transport through polymer films, it is not yet clear what ultimate rate can be achieved. In solar energy applications the important issue is whether the rate can be high enough so that the net electron transfer rate is light intensity limited. 

Holmlin RE, Haag R, Chabinyc ML, Ismagilov RF, Cohen AE, Terfort A, Rampi MA, Whitesides GM (2001) Electron transport through thin organic films in metal-insulator-metal junctions based on self-assembled monolayers. J Am Chem Soc 123 5075-5085... 

Figure 5. Transport through liquid film with chemical reaction.

Substrate transport through the film may be formally assimilated to membrane diffusion with a diffusion coefficient defined as12 Ds = Dch( 1 — 9)/pjort. In this equation, the effect of film structure on the transport process in taken into account in two ways. The factor 1—0 stands for the fact that in a plane parallel to the electrode surface and to the coating-solution interface, a fraction 9 of the surface area in made unavailable for linear diffusion (diffusion coefficient Dcj,) by the presence of the film. The tortuosity factor,, defined as the ratio between the average length of the channel and the film thickness, accounts for the fact that the substrate... 

Immobilizing the catalyst on the electrode surface is useful for both synthetic and sensors applications. Monomolecular coatings do not allow redox catalysis, but multilayered coatings do. The catalytic responses are then functions of three main factors in addition to transport of the reactant from the bulk of the solution to the film surface transport of electrons through the film, transport of the reactant in the reverse direction, and catalytic reaction. The interplay of these factors is described with the help of characteristic currents and kinetic zone diagrams. In several systems the mediator plays the role of an electron shuttle and of a catalyst. More interesting are the systems in which the two roles are assigned to two different molecules chosen to fulfill these two different functions, as illustrated by a typical experimental example. 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

Electroactive donors, such as TTF or triarylpyrazoline, can be bound in high yield to polymeric matrices. The TTF linear polymers show interesting cooperative properties (i.e., ion-radical cluster formation) that is not observed for the isolated monomers in solution or the low coverage polymers. Furthermore, thin solid films of these donors bound to cross-linked polymer backbones display remarkably facile charge transport through the film bulk which is accompanied by dramatic and reversible optical changes. 

If the two terms are of the same order of magnitude we may suspect that the gas film resistance affects the rate. On the other hand, if k J p is much smaller than kgS we may ignore the resistance to mass transport through the film. Example 18.1 illustrate this type of calculation. The results of that example confirm our earlier statement that film mass transfer resistance is unlikely to play a role with porous catalyst. 

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